ONCE apun a time, on the 26th of July, 1910, in the home of E. Pluribus and Minnie Dingbat, a lil' ''dollink'' of a Mouse beaned a small black Kat with the first of a series of billy-doos that took the form, most often, of a brick. The Mouse's name was Ignatz, the Kat was Krazy Kat, and by October 1913 Krazy and Ignatz had outgrown the Dingbat premises and moved to a comic strip all their own. In April 1916, ''Krazy Kat'' expanded to a full page in the arts and drama sections of the Sunday papers. Krazy's creator, George Herriman, was given a lifetime contract by William Randolph Hearst and a promise that the strip would always have a home in his newspapers, a bargain that was honored until Herriman's death in April 1944. Hearst was not alone in his regard for Herriman's genius. Long before Jay Cantor made Krazy Kat the heroine of his effervescent book ''Krazy Kat: A Novel in Five Panels,'' she was celebrated in a jazz-pantomime ballet choreographed by Adolph Bolm in 1922. In a famous essay published that year in Vanity Fair, the critic Gilbert Seldes rhapsodized: ''Krazy Kat, the daily comic strip of George Herriman, is, to me, the most amusing and fan-tastic and satisfactory work of art produced in America today. . . . Mr. Herriman, working in a despised medium, without an atom of pretentiousness, is day after day producing something essentially fine.'' Yet, despite the strip's longevity and the kudos that constantly accrued to it, Herriman's work did not enter the mainstream of comic-strip mythology, and for all her superior gifts, Krazy's fame has been outstripped by that of those so much more conventional felines: Felix, Tom, Fritz and Garfield.

FOR Krazy herself (who is, by the inspiration of Mr. Cantor, still alive and thinking in the Ill-easy-yum of Coconino County, Arizona), Garfield's success has been particularly galling:

''Cartoon cats today were just as popular as in her time, perhaps more so - some of the cats, she noticed, even got top banana position, the upper right-hand corner of the daily page, the first strip in the Sunday supplement. But those cats were cute! In her art she had instinctively revolted at that sickening state. . . . Think of it! To have so little dignity that you threw yourself like an infant on people's mercy, their protectiveness towards the bitty itsy thing - a tenderness that was only another face of their unconsidered overweening power. . . . And with all this sentimentality, she thought, came its ghost, its ugly shadow . . . obscenities like a book (she looked at the best-seller lists, too, for, after all, they had once been collected into a book) . . . a book . . . a book . . . she could hardly bear to think of it . . . a book of things to do with a dead cat.''

Clearly, Krazy ought to be setting an example to other cartoon cats, but though the stream of her consciousness is flowing at a steady pace, she is stopped in her tracks in the novel's first ''panel,'' or chapter - and not simply by George Herriman's death, but by a concurrent event, the testing of the first A-bomb at Alamogordo. For Krazy developed a platonic passion for the Father of the Bomb, J. Robert Oppenheimer, and so Krazy, who had always experienced Ignatz's bricks as missiles of love, tries to absorb Oppie's megabrick in the same blithe spirit. But she can't, and her thoughts are dark: ''We hug ourselves so we won't change and lose what we have - our fave TV show interrupted by: Bulletin: World Over! Everybody Dies! And art had become dead cats as lamps! Anything goes!''

Such is the basic premise of Mr. Cantor's novel-cum-homage, and the plot that is generated from that premise is, after a slow and somewhat bumpy takeoff, sprightly, delightful and insightful. How can an innocent albeit hedonistic Kat like Krazy go on being a professional ditz in an age of nuclear anxieties? Despondent Krazy's answer is that she can't. Mr. Cantor chronicles efforts by the ingenious Ignatz to get Krazy back into show biz and then achieve full employment for himself and the other residents of Coconino County.

In the second ''panel,'' Ignatz, like so many Jewish intellectuals of his generation, is a disciple of Freud and tries first to undertake a ''talking cure.'' He and Krazy free-associate like Astaire and Rogers, but not all of Ignatz's therapeutic techniques are verbal. As he confides to his clinical colleague Offissa Pup: ''This morning I began my first course of treatment for hysterical kats. I gave Krazy hydrotherapy, soaking her with the garden hose. No progress. In the afternoon, I tried electrotherapy. I shaved Krazy's tail; my son Irving jammed it into a light socket; and I stuck a bulb in her mouth to check the current. That made a nice kat lamp, but there wasn't much therapeutic gain I could see - she still doesn't want my delightful bricks. How queer!''

Members of the American Association of Electrotherapists may find such humor immature, and, similarly, members of Women Against Pornography will not be amused by the next chapter, or indeed by the rest of the book, which becomes steadily more ribald as the psychoanalyzed Kat tries to come to terms with S-E-X, despite the fact that no one in Coconino County, including Dr. Ignatz, understands what S-E-X involves. ''This sex,'' Krazy complains in one therapy session, ''is another gadget you boys have dreamed up. It connects everything with everything in a giant machine that bites and wets and sucks itself until there's one big explosion!''

In the third ''panel,'' Krazy, despite her skeptical views, cannot resist the lure of a starring role in a hypothetical movie that sea-changes from genre to genre until it has become all the movies ever made, in each of which Krazy plays goddess and whore: ''Kleo Kat on a marble slab, rubbed with luxurious eau de pamplemousse by a Nubian attendant. . . . Kleo rolled in a rug at the Producer's feet - for he himself plays Seizeher.''

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Then at the dizzying height of hope, a terrible discovery at the end of the chapter. The movie contracts that Krazy and Ignatz and the other Coconinoans have signed are worthless, for they don't own the rights to themselves: they are still owned by Hearst. ''And he won't sell! Not at a price a sane man can afford!''

This is not the first moment in his book that Mr. Cantor, whose first novel was ''The Death of Che Guevara,'' a book that imaginatively mixes fact and fiction about the Latin American revolutionary, becomes, as a good post-modernist should, self-referential. But it is certainly the crux of self-reference for such a novel as ''Krazy Kat,'' since all the while one is reading it, one can't help wondering: How did Mr. Cantor get to do this? Has Herriman's work fallen (as J. R. R. Tolkien's trilogy did, by a famous glitch) into the public domain? Not entirely, it would seem, for the front matter of the book states that the names of the characters are used with special permission of King Features Syndicate. It is one of the oddest anomalies of the law, as it applies to novelists, that while a writer may freely use living public figures such as Richard Nixon or Norman Mailer or the Vatican bank's Archbishop Paul Marcinkus as characters in works of fiction, copyright law protects figures of contemporary mythology like Mickey Mouse or Superman or James Bond from a similar fate. The creatures of our imaginations are our cat-tales, oops, make that our chat-tels. Were it otherwise, ''Krazy Kat'' would not be the very singular work it is, for profiteers would long since have saturated the market with every conceivable rip-off: pornographic escapades of Mickey and Minnie, tales of Holden Caulfield's college years and thousands of ''Star Trek'' novels instead of the mere 40-odd that exist now.

AS Mr. Cantor's comedy becomes bawdier and bolder (the fourth and funniest ''panel'' of all tells of Krazy's tribulations as the Patty Hearst-like hostage of a parody Symbionese Liberation Army led by Ignatz, determined to win the rights to himself and the others), his cartoon characters become rounder, richer, more densely packed with varies-him-altitude, until in the last ''panel,'' Kat and Ignatz have become proper human beings and popular successes once again, as a singer-pianist duo. They live at the Plaza and entertain themselves by reading aloud to each other their rave reviews in The New York Times and Variety and in the pages of an unnamed glossy magazine, whose critic, in an apotheosis of pre-emptive self-appreciation unequaled since John Irving's ''World According to Garp,'' explicates the moral of the story and the secret of their success. Since Mr. Cantor seems so eager to have the last word concerning his own achievement (though it is a collaboration as much as Kat's and Ignatz's achievement is), and since his imaginary critical brick is right on target, I will let his own (and Herriman's) critic Don Kiyoti explain what the performance of Kat and Ignatz was all, so agreeably, about:

''Kat and Ignatz show us that you can participate in your lover's [ read: co-author's ] success - and the electricity between these two is palpable; we can be certain that these two are lovers. She moves away from him, accompanied by the blues notes on the piano, as he mourns for her loss. But, won by his feelingful playing, his empathy for her - the way he embodies her in the song - she turns towards him with the melody. A game of hide and seek. In art - sharing the creation of a fantasy - they achieve their fusion with each other, drinking each other from the same cup, a cup they have created while we watched.'' HER BRILLIANT CAREER

In ''Krazy Kat,'' Jay Cantor's

X-rated sort-of-sequel to the comic strip, Krazy and Ignatz spend a lot of time trying to escape their two-dimensional characters and become ''rounded.''

A lot of their tries are sexual, and a lot of their sex involves dominance. But, as Mr. Cantor explained in a telephone interview from his home in Cambridge, Mass., Krazy has to ''experiment with the roles of submission and dominance in order to work free of these roles.'' For years Krazy had submitted to the bricks Ignatz had thrown at her, bricks she had seen as love tokens. ''She discovers that if she wants power,'' Mr. Cantor said, ''she must act for herself. We are not talking about sexual power, but the power to build her own artistic career. We would like sexuality to be about love but often it is about power. She has to explore her need and desire for power first.''

Mr. Cantor, who is 39 years old, conducts a fiction-writing workshop at Tufts University and teaches a course on Freud, Marx and Nietzsche (''Together again for the first time,'' he said, quoting an old joke).

He bought the rights to use Krazy Kat from King Features Syndicate Inc. ''At the time, I did not have specific plans, but I wanted to get inside the world of a comic strip. I consider my entertainment a serious business.'' His previous novel, ''The Death of Che Guevara,'' had been ''a heavy weight I had carried around for 12 years,'' he said. ''I wanted to explore other areas.'' BARTH HEALEY

Thomas M. Disch's most recent books are the computer-interactive novel ''Amnesia'' and the forthcoming children's book ''The Brave Little Toaster Goes to Mars,'' a sequel to ''The Brave Little Toaster.''

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A version of this review appears in print on January 24, 1988, on Page 7007001 of the National edition with the headline: REFUSING TO BE A PUSSYCAT. Today's Paper|Subscribe